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A
600 pF capacitor is charged by a 200 V supply. It is then
disconnected from the supply and is connected to another uncharged
600 pF capacitor. How much electrostatic energy is lost in the
process?

In the circuit shown in figure, charge stored in $6\mu F$ capacitor will be

A string attached to a light thread is whirled in a vertical circle with a constant velocity $v$. The radius of the circle is $10\text{m}$. The maximum and minimum tension of the string is in the ratio $4:1$. What is the value of velocity $v$?

(Take $g=10{\text{m/s}}^2$)

If work done by the heat engine is $600\text{J}$ and heat absorbed by the working substance is $800\text{J}$, the efficiency of the heat engine is

A proton and an alpha particle both enter a region of uniform magnetic field $B$, moving at right angles to the field $B$. If the radius of circular orbits for both the particles is equal and the kinetic energy of the proton is $1MeV$, the energy of the alpha particle will be

If 6 andα are the roots of the equation $x^2$ - ax + 30 = 0, find the value of α.

A block of mass $10kg$ is pulled at constant speed on a rough horizontal surface by a force of $19.6N$. The coefficient of friction is

The equation of a plane progressive wave is $y=0.09\text{sin}8\pi (t-\frac{x}{20})$. When it is reflected at rigid support, its amplitude become ${\frac{2}{3}}^{rd}$ of its previous value. Then the equation of the reflected wave is

Figure shows a metallic wire of resistance $0.20\Omega$ sliding on a horizontal, U-shaped metalic rail. The separation between the parallel arms is 20 cm. An electric current of $2.0\mu$ A passes through the wire when it is slid at a rate of $20cm{s}^{-1}$. If the horizontal component of the earth's magnetic field is $3.0\times {10}^{-5}$ T, Calculate the dip at the place.

Particle A starts from rest at t = 0 from x = 0 with constant acceleration to reach x = 1 m at t = 1 s. Particle B starts with uniform velocity at t = 0 from x = 1 to reach x = 2m at t = 1 s. What will be the distance covered by particle B in the frame of reference attached to particle A from t = 0 to t = 1 s. (upto two decimal places in meter)

The near point and far point of a person are $40\text{cm}$ and $200\text{cm}$ respectively. Find the power of the lens he/she should use while reading at $25\text{cm}$

How many
significant figures should be present in the answer of the following
calculations?

(i)

(ii) 5 ×
5.364

(iii)
0.0125 + 0.7864 + 0.0215

A body is traveling in a circle of radius 10 cm as shown. What is the ratio of the average speed to the average velocity when it reaches N from M in a clockwise direction along the circumference of the circle in 1 min?

If $x=asin[\omega t+\frac{\pi }{6}]and{x}^{\prime }=acos\omega t$, then what is the phase difference between the two waves?

A ball whose kinetic energy is E, is thrown at an angle of ${45}^{\circ }$ with the horizontal. Its kinetic energy at the highest point of its trajectory will be

Let an $AC$ circuit contains a capacitor of capacitance $C=100\mu \text{F}$ only. If the instantaneous current in the circuit is $i=1.57\sin 100\pi t$. The expression for the instantaneous voltage, $E$ at this instantacross the capacitor will be

At two points $P$ and $Q$ on a screen in Young's double slit experiment, waves from slits $S_1$ and $S_2$ have a path difference of $0$ and $\frac{\lambda }{4}$ respectively. The ratio of intensities at $P$ and $Q$ will be:

In a projectile motion, the position vector is given by $\overrightarrow{r}=6t\hat{i}+(8t-5t^2)\hat{j}$; the range is

A rod of mass m is supported on a wedge of mass M as shown in figure. Find the accelerations of rod a and wedge A in the arrangement. Assume that the friction between all contact surfaces is negligible.

A block of mass $m$ is kept on an inclined plane inside a lift moving down with acceleration of $2{\text{m/s}}^2$. What should be the coefficient of friction between block and inclined plane to let the block move down with constant velocity relative to lift?

(Take $g=10{\text{m/s}}^2$)

A person is sitting in a train which is moving with an acceleration of 10 m/$s^2$ rightwards. A pendulum is hanging from the ceiling

(P) Draw the Free Body Diagram of the bob with respect to the person sitting in the train.

(Q) Draw the same with respect to a person who's standing outside.

Momentum of a photon of wavelength $\lambda$ is

In a Young's double slit experiment, the distance between the slits & the screen is $100\text{cm}.$ For a certain distance between the slits, an interference pattern is observed on the screen with the fringe width $0.25\text{mm}$. When the distance between the slits is increased by $1.2\text{mm},$ the fringe width decreased to $2/3$ of the original value. In the final position, a thin glass plate of refractive index $1.5$ is kept in front of one of the slits & the shift of central maximum is observed to be $20$ times the initial fringe width. Find the thickness of the plate.

A small uniform rod AB of mass M and length l rotates freely with angular velocity ${\omega }_0$ in a horizontal plane about a vertical axis passing through one of its end A. A small sleeve of mass M starts sliding along the rod from A. Angular velocity of rod when sleeve reaches the other end, is

Three-blocks $A$,$B$ and $C$ of mass $4\text{kg}$, $2\text{kg}$ and $1\text{kg}$ respectively are in contact of a frictionless surface as shown. If a force of $14\text{N}$ is applied on the $4\text{kg}$ block, then the contact force between $A$ and $B$ will be

A bullet of mass 50g and specific heat capacity $800k{g}^{-1}{K}^{-1}$is initially at a temperature ${20}^{\circ }C.$ It is fired vertically upwards with a speed of $200m{s}^{-1}$and on returning to the starting point strikes a lump of ice at $0^{\circ }C$ and gets embedded in it. Assume that all the energy of the bullet is used up in melting. Neglect the friction of air. Latent heat of fusion of ice $=3.36\times {10}^{5}Jk{g}^{-1}$

A train approaching a railway crossing at a speed of $120{\text{kmh}}^{-1}$ sounds a short whistle at frequency $640\text{Hz}$, when it is $300\text{m}$ away from the crossing. The speed of sound in air is $340{\text{ms}}^{-1}$. What will be frequency heard by a person standing on a road perpendicular to the track through the crossing at a distance of $400\text{m}$ from the crossing ?

Why centripetal acceleration is also called as normal acceleration?

1. 1575

A projectile is projected at an angle of ${45}^{\circ }$ to the horizontal. The slope of trajectory of the body varies with time $t$ as